Method and apparatus for feature domain joint channel and additive noise compensation

ABSTRACT

A method for performing noise adaptation of a target speech signal input to a speech recognition system, where the target speech signal contains both additive and convolutional noises. The method includes estimating an additive noise bias and a convolutional noise bias; in the target speech signal; and jointly compensating the target speech signal for the additive and convolutional noise biases in a feature domain.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is a continuation-in-part of United States patent application Ser. No. 09/628,376 filed on Jul. 31, 2000, which itself is a continuation-in-part of U.S. patent application Ser. No: 09/551,001 filed Apr. 18, 2000, both of which are hereby incorporated by reference in their entirety.

FIELD OF THE INVENTION

[0002] The present invention relates to automatic speech recognition systems. More particularly, the invention relates to technique for adapting the recognizer to perform better in the presence of noise.

BACKGROUND OF THE INVENTION

[0003] Current automatic speech recognition systems perform reasonably well in laboratory conditions, but degrade rapidly when used in real world applications. One of the important factors influencing recognizer performance in real world applications is the presence of environmental noise that corrupts the speech signal. A number of methods, such as spectral subtraction or parallel model combination, have been developed to address the noise problem. However, these solutions are either too limited or computationally expensive.

[0004] Recently, a Jacobian adaptation method has been proposed to deal with additive noise, where the noise changes from noise A to noise B. For example, U.S. Pat. No. 6,026,359 to Yamaguchi describes such a scheme for model adaptation in pattern recognition, based on storing Jacobian matrices of a Taylor expansion that expresses model parameters. However, for this model to perform well, it is necessary to have noise A and noise B close to one another in terms of character and level. For example, the Jacobian adaptation technique is likely to work well where noise A is measured within the passenger compartment of a given vehicle traveling on a smooth road at 30 miles per hour, and where noise B is of a similar character, such as the noise measured insude the same vehicle on the same road traveling at 45 miles per hour.

[0005] The known Jacobian adaptation technique begins to fail when noise A and noise B lie far apart from one another, such as when noise A is measured inside the vehicle described above at 30 miles per hour and noise B is measured in the vehicle with windows down or at 60 miles per hour.

[0006] This shortcoming of this known Jacobian noise adaptation technique limits its usefulness in many practical applications because it is often difficult to anticipate at training time the noise that may be present at testing time (when the system is in use). Also, improvements in Jacobian noise adaptation techniques are limited in many applications because the computational expense (processing time and/or memory requirements) needed makes them impractical.

[0007] Another concern relates to compensation of convolutional noise. Convolutional noise can be distinguished from the above-discussed additive noise in that convolutional noise results from the speech channel. For example, changes in the distance from the speaker to the microphone, microphone imperfections, and even a telephone line over which the signal is transmitted all contribute to convolutional noise. Additive noise, on the other hand, typically results from the environment in which the speaker is speaking.

[0008] An important characteristic of convolutional noise is that it is multiplicative when the speech signal is in the spectral domain, whereas additive noise is additive in the spectral domain. These characteristics cause particular difficulties with respect to noise compensation. In fact, most conventional approaches deal either with convolutional noise or additive noise, but not both.

SUMMARY OF THE INVENTION

[0009] Therefore, one configuration of the present invention provides a method for performing noise adaptation of a target speech signal input to a speech recognition system, where the target speech signal contains both additive and convolutional noises. The method includes estimating an additive noise bias and a convolutional noise bias; in the target speech signal; and jointly compensating the target speech signal for the additive and convolutional noise biases in a feature domain.

[0010] Another configuration of the present invention provides a speech recognition apparatus that includes noise adaptation of a target speech signal input to the apparatus, where the target speech signal contains both additive and convolutional noises. The apparatus is configured to estimate an additive noise bias and a convolutional noise bias in the target speech signal; and jointly compensate the target speech signal for the additive and convolutional noise biases in a feature domain.

[0011] Configurations of the present invention are more robust against nonstationary noise and channels, fewer parameters are modified at each iteration, and only signal features are modified rather than all model features. Therefore, configurations of the present invention use less memory (e.g., random access memory or RAM), which is advantageous for small embedded systems. Moreover, because the model features are not modified, adapted model features need not be stored in memory.

[0012] Further areas of applicability of the present invention will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The present invention will become more fully understood from the detailed description and the accompanying drawings.

[0014]FIG. 1 diagrammatically represents different noise conditions, useful in understanding the invention.

[0015]FIG. 2 is a data flow diagram of both training and recognition phases, illustrating a presently preferred implementation of the improved Transformed Matrix adaptation.

[0016]FIG. 3 is a log-spectral plot comparing conventional Jacobian Adaptation with Parallel Model Combination (PMC) adaptation.

[0017]FIGS. 4 and 5 are α-adaptation parameter curves, showing the effect of different α values upon recognition accuracy.

[0018]FIG. 6 is a block diagram of one configuration of a noise adaptation system of present invention.

[0019]FIG. 7 is a block diagram of one configuration of a feature Jacobian adaptation module of the present invention.

[0020]FIG. 8 is a block diagram of one configuration of a convolutional noise module utilizing the feature Jacobian adaptation module of FIG. 7.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0021] The following description of the preferred embodiment(s) is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses.

[0022] At least one configuration of the present invention is applicable to the problem diagrammatically illustrated in FIG. 1. As shown in 10, assume, for example, that the automatic speech recognition system must work with a noisy environment, such as within a passenger compartment of a moving vehicle. The noise level measured within the passenger compartment typically increases from noise A to noise A′ as the vehicle speeds up. Although the noise level may increase from A to A′, the character or quality of the noise remains largely the same. In a moving vehicle, for example, the noise spectrum typically changes in a predictable way as the vehicle speeds up. Wind noise increases in amplitude, but retains its largely random white noise or pink noise character. Road surface noise (the sound of the tires rolling upon the road surface) increases in frequency in proportion to the increase of noise.

[0023] Unfortunately, in many real world applications, the character and quality of the ambient noise cannot be as readily predicted as the conditions at 10 in FIG. 1 might imply. Consider the portable cellular telephone, for example. The cellular phone may be used in a moving vehicle where it experiences the range of noises illustrated at 10; or it may be used on a street corner where completely different traffic sounds abound; or it may be used in a shopping mall with yet an entirely different noise quality. This wide diversity in different noise qualities is illustrated in FIG. 1 at 12, where three different noise patterns have been diagrammatically depicted as noise A, noise B, and noise C. The unpredictability of noise quality has heretofore presented a significant challenge for automatic speech recognition systems that must perform in these varied noisy environments.

[0024]FIG. 2 illustrates an exemplary embodiment of the invention in a speech recognition application. The speech recognition application employs a model-based recognizer. The models are developed during training and are then later used during recognition. In FIG. 2, the training phase of the system is illustrated generally at 20 and the recognition phase at 40. Input speech is provided during the training phase under noise condition A, as illustrated at 22. The input speech is used to train speech models as indicated at step 24, with exemplary speech models diagrammatically represented at 26. In the typical input speech signal there will be times during which no speech is present, such as prior to the beginning of speech or after the end of speech. These non-speech portions may be used to record data indicative of the reference noise N_(a) that is associated with noise condition A. In FIG. 2, the reference noise N_(a) is stored at block 28. If desired, the noise may be modeled (background model) using the same training operation used to construct the speech models 26.

[0025] After training the speech models, a set of Transformed Matrices is calculated at step 30 and stored at 32. These matrices are used during recognition to adapt the speech models so that they will perform better under the noise conditions existing during recognition. The basic Jacobian adaptation process assumes that the quality of the noise during recognition time is approximately the same as during training time. Otherwise, classic Jacobian adaptation may produce less than optimal results.

[0026] The improved adaptation technique is based on the use of a set of Transformed Matrices generated for the initial noise condition N_(a). The Transformed Matrices are computed by applying a linear or non-linear transformation to a set of the Jacobian matrices developed for the initial noise condition N_(a). The presently preferred embodiments perform the transformation (both linear and non-linear) by applying an α-adaptation factor as presented in the next section. While the α-adaptation factor is presently preferred, a neural network or other artificial intelligence component may be used to effect the transformation.

[0027] The manipulation of matrices can be a highly computationally expensive process. A considerable cost factor is the memory space needed to store all of the matrices. In a typical embodiment, the speech models for each entry in the lexicon may employ multiple Hidden Markov Model states, with multiple Gaussian densities associated with each state. There would thus be one matrix for each of the Gaussians in each of the states. This could result in several hundred matrices needing to be stored.

[0028] The preferred embodiment performs a matrix decomposition step 36 to generate a reduced-complexity set of Jacobian matrices 38. As will be more fully discussed below, the presently preferred decomposition technique uses principal component analysis (PCA) to construct the reduced-complexity Transformed Matrices.

[0029] At recognition time, input speech from the user is provided at step 42. The input speech is associated with a noise condition B (also referred to as the target noise N_(b)) as illustrated at 44. As previously discussed, if the noise condition B is different in quality from the noise condition A used at training time, the traditional Jacobian adaptation technique may produce less than optimal results. However, we have found that the α-adaptation process (performed when the Jacobian matrices are defined during training) greatly improves recognition performance under adverse noise conditions. Results of our tests are provided in the example presented below.

[0030] The target noise N_(b), shown at 44 in FIG. 2, is extracted from the input speech 42 and then used to calculate the difference from the reference noise N_(a) as indicated at 46. New adapted speech models are then calculated using this noise difference and the reduced Transformed Matrices developed during training, as illustrated at 48. The resulting adapted speech models 50 are then used at 52 to perform speech recognition on the input speech 42 to provide the recognition output 54.

[0031] Alpha Adaptation

[0032] To better appreciate how our Transformed Matrices work, it is useful to understand conventional Jacobian adaptation. Conventional Jacobian adaptation is related to another form of adaptation known as parallel model combination (PMC). Traditionally, Jacobian adaptation is used as an approximation for PMC, in order to reduce the computational burden that PMC requires. PMC is highly computationally expensive because, for each density of the speech model, mean vectors must be transformed into the spectral domain. Then, after adding the mean vector to the target noise, the resulting vector must be transformed back into the cepstral domain. This double transformation, which makes use of a matrix multiplication and of two non-linear functions, is usually too time consuming for embedded systems.

[0033] Traditionally, Jacobian adaptation is used as an approximation of PMC in the cepstral domain. For comparison purposes, equation (1), reproduced below, describes the PMC calculation, where capital F represents the matrix of Discrete Cosign Transform (DCT). Equation (2) represents the traditional Jacobian adaptation calculation that is used as an approximation of the more computationally costly PMC calculation. $\begin{matrix} {{C\left( {S + N} \right)} = {{F \cdot {\log \left( {\exp \left( {F^{- 1} \cdot {C(S)}} \right)} \right)}} + {\exp \left( {F^{- 1} \cdot {C(N)}} \right)}}} & (1) \\ {{\Delta \quad {C\left( {S + N} \right)}} = {{{\frac{\partial{C\left( {S + N} \right)}}{\partial{C(N)}} \cdot \Delta}\quad {C(N)}} = {{F \cdot \frac{N}{S + N} \cdot F^{- 1} \cdot \Delta}\quad {C(N)}}}} & (2) \end{matrix}$

[0034] The problem with the Jacobian adaptation approximation is that it holds only where the target noise (experienced during system use) is similar in quality to the reference noise (present during system training). The nature of the problem is illustrated in FIG. 3, which plots the evaluation, in the log-spectral domain, of the noisy speech parameters when the noise increases. Specifically, the plots show in the log-spectral domain how PMC adaptation and conventional Jacobian adaptation compare. In FIG. 3 the shaded region on the left corresponds to the condition where the speech signal is far more powerful than the noise, whereas the region on the right corresponds to conditions where the noise is more powerful than the speech signal. If both the training and testing environments are in the same of these two regions, then Jacobian Adaptation and PMC perform similarly. However, if one of these two environments is in the middle region, or if it is in another region than the other environment, then Jacobian Adaptation differs from PMC, and actually always underestimates the adaptation of the models.

[0035] We have discovered that the conventional Jacobian adaptation can be greatly improved through a linear or non-linear transformation of the Jacobian matrices. To effect the linear or non-linear transformation, the preferred embodiments employ a parameter that we call an α-adaptation parameter. Equation (3) below illustrates the presently preferred use of the α-adaptation parameter to effect a non-linear transformation. Equation (4) shows an alternate use of the parameter to effect a linear transformation. As noted above, while the use of an a-adaptation parameter to effect the transformation is presently preferred, other transformation techniques are also possible. For example a neural network or other artificial intelligence component may be used to transform Jacobian matrices for the initial noise condition. Another transformation technique involves applying a first cc-adaptation parameter or factor to the input speech and a second α-adaptation parameter or factor to the noise. Other variations are also possible. $\begin{matrix} {{\Delta \quad {C\left( {S + N} \right)}} = {{F \cdot \frac{\alpha \quad N}{S + {\alpha \quad N}} \cdot F^{- 1} \cdot \Delta}\quad {C(N)}}} & (3) \\ {{{JA}:\quad {\Delta \quad {C\left( {S + N} \right)}}} = {{\frac{\partial{C\left( {S + N} \right)}}{\partial{C(N)}} \cdot {\alpha\Delta}}\quad {C(N)}}} & (4) \end{matrix}$

[0036] Referring to equation (3), the α-adaptation parameter functions as follows. If the reference noise is close to zero, and if α is not too large, then both tangents (computed respectively at x-coordinate N and αN) are horizontal. If the reference noise is very important, then both tangents will correspond to the line y=x. If the reference noise belongs to the central region of FIG. 3, then the new slope of the tangent will be greater than the conventional Jacobian adaptation curve would have produced.

[0037] Use of the α-adaptation parameter in equation (3) results in a non-linear transformation of the matrices. Both numerator and denominator are multiplied by the parameter, hence producing a non-linear transformative effect. In equation (4) the α-adaptation parameter is multiplied against the resulting numerator/denominator quotient, hence producing a linear transformative effect.

[0038] In both cases, the main effect of the α-adaptation parameter is to increase the adaptation bias added to the speech models. This is useful because it corrects the shortcoming of conventional Jacobian adaptation to underestimate the effect of noise. In a later section of this document we present our experimental results, showing the improvements which are possible using the adaptation parameter.

[0039] Selection of the α-Adaptation Parameter

[0040] Theoretically, the optimal value of the a-adaptation parameter is dependent on the environment: the value for a should be greater where the mismatch between target noise and reference noise is greater. However, we have discovered that the α-adaptation parameter is far more stable than theory would have predicted. When used to generate Transformed Matrices as a replacement for conventional Jacobian adaptation, the variation in speech recognition accuracy is low for small values of α, increases for medium values of α and becomes low again when α increases beyond a certain point. This phenomenon is due to the shape of the curve in FIG. 3. Specifically, whatever the value of α is, the slope of the tangent will only vary between 0 and 1.

[0041] To clarify this point, we have realized a set of experiments for digits recognition in adverse environments. Twelve context-independent models of digits were constructed: the numbers from 1 to 9 plus models for “o” and “zero”, plus a model for silence. The silence was modeled by a Hidden Markov Model (HMM) with five states. The remaining models used fifteen states. Each state of all the HMMs employs four Gaussian densities. The training set used to train the models comprised 3803 sequences of digits, pronounced by 80 speakers. The training set was recorded under laboratory conditions without noise. FIGS. 4 and 5 represent the variation of accuracy when α is varied in a range from 1 to 4. The data was generated based on six different acoustic environments:

[0042] The validation corpus, which is recorded in clean conditions.

[0043] The same corpus, with added car noise with a SNR of 10 dB.

[0044] The same corpus, with added car noise with a SNR of 0 dB.

[0045] The same corpus, with added white noise with a SNR of 15 dB.

[0046] The test corpus, recorded in a car at 30 mph.

[0047] Another test corpus, recorded in a car at 60 mph.

[0048] Referring to FIGS. 4 and 5, it can be seen that whatever the acoustic environment is, the variation of accuracy for different values of α is very low in the range of α=2.4 to α=3.6. This shows that α has a stable range that may be suitably exploited in a practical embodiment of the invention. While we presently prefer an α-adaptation parameter between about 2.4 to 3.6, it will be understood that this is merely representative of one possible stable range. In general, other values of a may be used with beneficial results. Stated differently, the decrease of accuracy between the true “optimal” value of α and any other value of α that may be chosen in a considered range (e.g. 2.4-3.6) is very low. Our data shows that the decrease in accuracy from the “optimal” point is less than three percent. This makes our improved Jacobian adaptation a very robust method.

[0049] Dimensionality Reduction for Reducing Computational Expense

[0050] As noted above, although Jacobian adaptation is less computationally expensive than PMC, it still places a fairly taxing burden on the recognition system, particularly for embedded systems.

[0051] Indeed, we have seen that each Tranformed Matrix can be expressed by the following equation (5): $\begin{matrix} {{\frac{\partial{C\left( {S + N} \right)}}{\partial{C(N)}} \cdot} = {F \cdot \frac{S + {\alpha \quad N}}{\alpha \quad N} \cdot F^{- 1}}} & (5) \end{matrix}$

[0052] where $\frac{S + {\alpha \quad N}}{\alpha \quad N}$

[0053] is a diagonal matrix with dimensions NFilt X NFilt, where Nfilt is a N the number of filters used in the spectral filter-bank.

[0054] Thus, each Transformed Matrix can be expressed as the weighted sum of Nfilt canonical matrices, which are in fact a base of the space to which Jacobian matrices belong. These canonical matrices are defined by: J_(i)=F·diag(i)·F⁻¹ where diag(i) refers to a diagonal Nfilt x Nfilt matrix with 0 everywhere but 1 at position i.

[0055] Each Transformed Matrix can thus be expressed as: $\begin{matrix} {\frac{\partial{C\left( {S + N} \right)}}{\partial{C(N)}} = {\sum\limits_{i = 1}^{Nfilt}{\gamma_{i} \cdot J_{i}}}} & (6) \end{matrix}$

[0056] Thus, instead of storing Nd matrices (where Nd is the total number of densities in all the speech models), it is enough to store Nfilt canonical matrices, plus Nd times Nfilt coefficients γ_(i). This considerably decreases the storage requirements.

[0057] However, this solution can be further improved because it increases the time-complexity of the algorithm: indeed, when all the Transformed Matrices are stored, equation (2) can be applied directly to all the densities, which costs Nd matrix multiplication.

[0058] If the second solution is chosen, the right part of equation (2) becomes: ${{\frac{\partial{C\left( {S + N} \right)}}{\partial{C(N)}} \cdot \Delta}\quad {C(N)}} = {{{\left( {\sum\limits_{i = 1}^{Nfilt}{\gamma_{i} \cdot J_{i}}} \right) \cdot \Delta}\quad {C(N)}} = {\sum\limits_{i = 1}^{Nfilt}{\gamma_{i} \cdot {\left( {{J_{i} \cdot \Delta}\quad {C(N)}} \right).}}}}$

[0059] In this equation, the cost is Nfilt matrix additions, and Nfilt matrix multiplication by a scalar: this must be repeated for each density. The total cost is thus 2·Nd·Nfilt matrix operations.

[0060] If we do not want to use extra computational time, the number of canonical matrices has to be reduced.

[0061] The presently preferred technique to reduce the dimension of a space is to realize a Principal Component Analysis on the set of elements belonging to this space. We have thus first computed all the vectors and $\frac{S + {\alpha \quad N}}{\alpha \quad N}$

[0062] and realized a single value decomposition on this set of vectors. The resulting canonical vectors have been used to compute the Nfilt canonical Jacobian matrices $F \cdot \frac{S + {\alpha \quad N}}{\alpha \quad N} \cdot F^{- 1}$

[0063] sorted with descending order of their eigenvalues.

[0064] Using principal component analysis, as described above, can yield considerable improvement in reducing computational burden. Experiments have shown that it is possible to reduce the number of useful canonical matrices down to five matrices. Even further reduction may be possible. Reducing the number of matrices decreases the space requirements as well as the computation time needed to perform the adaptation. To better understand the improvement achieved through dimensionality reduction (principal component analysis) Table I compares the Transformed Matrix adaptation process both with and without employing principal component analysis. TABLE I dim. alpha Clean 30 mph 60 mph Comp. time Without PCA 32 2 98.74% 95.29% 90.21% 2439.28 us With PCA 7 2.4 98.56% 95.70% 90.63% 1932.42 us

[0065] In the above Table I the first column identifies the number of dimensions, that is the number of canonical matrices. The next column identifies the α-adaptation value used. The remaining columns give the percentage of recognition accuracy and the associated computation time required (cumulative time in, microseconds, of the adaptation over the whole database) for the following three environmental conditions: clean (no noise), vehicle at 30 miles per hour and vehicle at 60 miles per hour.

[0066] Experimental Results

[0067] The noise adaptation techniques described in the foregoing were tested under various noise conditions. The results of our tests are reproduced in this section. To test the adaptation system a speech recognizer for a car navigation system was employed. Of course, the adaptation techniques described herein are not restricted to car navigation or any other recognition task. Car navigation was selected for our tests because noise conditions within a moving vehicle can vary quite widely over different vehicle speeds. Thus a test of the adaptation system in a vehicular environment was selected as a good measure of the adaptation system's capabilities.

[0068] The experimental setup of these experiments is the same as previously described. Three testing sets were constructed: (1) comprising a validation set, composed of 462 sequences of digits pronounced by 20 speakers (different than in the training set), recorded in the same conditions as used in the training set; (2) composed of 947 sequences of digits pronounced by different speakers and recorded in a car at 30 miles per hour; (3) composed of 475 sequences of five digits pronounced by the same speakers, but recorded in the car at 60 miles per hour.

[0069] Recognition was performed using a simple loop grammar, with equal transition probabilities for all the numbers (“o” and “zero” models the same number) and silence. Accuracy was computed on ten numbers, after removing the silences in the recognized sentences.

[0070] For these first experiments, the signal was coded into a sequence of vectors of nine PLP coefficients (including the residual error) plus nine delta coefficients. Adaptation, if performed, was applied to only the means of the first nine static coefficients. For adaptation, the target noise was computed using 30 first frames of each sentence.

[0071] The results reproduced in Table II below, compare the performance of the Hidden Markov Models (HMM) without adaptation with the results obtained using parallel model combination (PMC) and traditional Jacobian adaptation (JA). Table II thus shows how both parallel model combination and Jacobian adaptation improve recognition performance in the presence of noise. Table II does not, however, show the performance of the improved Transformed Matrix adaptation using α-adaptation. This table is presented to serve as a baseline against which the improved Transformed Matrix adaptation technique may be better understood. TABLE II system Clean validation 30 mph 60 mph HMM (no adaptation) 98.84% 56.27% 35.83% PMC 95.78% 91.72% 89.60% JA 98.66% 83.76% 70.02%

[0072] TABLE III Adaptation alpha clean 30 mph 60 mph No 98.84% 56.27% 35.83% PMC 95.78% 91.72% 89.60% JA 98.66% 83.76% 70.02% α-PMC 1.3 96.03% 91.67% 89.81% α-TM 3 98.73% 95.24% 89.81%

[0073] Table III shows the comparative performance of both parallel model combination and Jacobian adaptation, with and without the alpha factor. In Table III the Transformed Matrix adaptation with α-adaptation is designated “α-TM.” For comparison purposes, the alpha factor was also applied in the parallel model combination technique as shown in the row designated “α-PMC.”

[0074] Comparing the results in Table III, note that the improved Transformed Matrix adaptation (α-TM) performs significantly better than standard Jacobian adaptation (JA) in the presence of noise. While the alpha factor did not substantially degrade the performance of PMC adaptation, it did not provide significant improvement either.

[0075] The results of our experiments show that the improved Transformed Matrix adaptation technique, employing the α-adaptation factor, gives considerably better results that standard Jacobian adaptation. Moreover, because Transformed Matrix adaptation is inherently less computationally expensive than PMC, it becomes an ideal candidate for embedded recognition systems that do not have a lot of processing power or memory. Such applications include, for example, cellular telephone recognition systems and vehicular navigation systems and other consumer products.

[0076] In addition, still further improvements in system performance can be had through use of the dimensionality reduction techniques described herein. When combined with Transformed Matrix adaptation, the result is a compact, efficient and robust adaptation system that will serve well in many recognition applications.

[0077] Further Embodiments

[0078] It will be appreciated that while the above discussion demonstrates the advantages of α-Jacobian adaptation for additive noise, similar advantages can be achieved with respect to convolutional noise. At the outset, it is important to note that in practice, all speech signals are corrupted, not only by additive noise, but also by convolutional (or channel) noise. The classical equation that represents the resulting signal, in the spectral domain, is S′=HS+N, where S is the spoken speech, S′ is the resulting signal, H is the channel noise and N is the additive noise. Written in the cepstral domain, this equation becomes C(S′)=C(HS+N).

[0079] Let us define H_(tar) and N_(tar′) respectively, as the target convolutional and additive noises (i.e., estimated at testing time), and H_(ref) and N_(ref), respectively, as the reference convolutional and additive noises (i.e., estimated at training time). Then, we can compute: ${C\left( {{H_{tar}S} + N} \right)} = {C\left( {\frac{H_{tar}}{H_{ref}}\left( {{H_{ref}S} + {\frac{H_{ref}}{H_{tar}}N_{tar}}} \right)} \right)}$ ${C\left( {{H_{tar}S} + N_{tar}} \right)} = {{C\left( \frac{H_{tar}}{H_{ref}} \right)} + {{C\left( {{H_{ref}S} + {\frac{H_{ref}}{H_{tar}}N_{tar}}} \right)}.}}$

[0080] Jacobian approximation (or α-Jacobian approximation) can then be applied to the second term of the sum: ${C\left( {{H_{ref}S} + {\frac{H_{ref}}{H_{tar}}N_{tar}}} \right)} = {{C\left( {{H_{ref}S} + N_{ref}} \right)} + {\frac{\partial{C\left( {{H_{ref}S} + N_{ref}} \right)}}{\partial{C\left( N_{ref} \right)}}\left( {{C\left( {\frac{H_{ref}}{H_{tar}}N_{tar}} \right)} - {C\left( N_{ref} \right)}} \right)}}$ ${C\left( {{H_{ref}S} + {\frac{H_{ref}}{H_{tar}}N_{tar}}} \right)} = {{C\left( {{H_{ref}S} + N_{ref}} \right)} + {J_{c}\left( {{C\left( N_{tar} \right)} - {C\left( N_{ref} \right)}} \right)} - {J_{c}\left( {{C\left( H_{tar} \right)} - {C\left( H_{ref} \right)}} \right)}}$

[0081] where $J_{c} = \frac{\partial{C\left( {{H_{ref}S} + N_{ref}} \right)}}{\partial{C\left( N_{ref} \right)}}$

[0082] denotes the Noise adaptation matrix of speech vector S.

[0083] Thus,

C(H _(tar) S+N _(tar))=(1−J _(c))(C(H _(tar))−C(H _(ref)))+C(H _(ref) S+N _(ref))+J_(c)(C(N _(tar) −C(N _(ref)))  (7)

[0084] The first term (1−J_(c))(C(H_(tar))−C(H_(ref))) represents the convolutional bias (C(H_(tar))−C(H_(ref)))transformed by a channel adaptation matrix (1−J_(c)). It is important to note that the transformation is of the convolutional bias as represented in the cepstral domain. The third term J_(c)(C(N_(tar))−C(N_(ref))) represents the additive bias transformed by a noise adaptation matrix J_(c). The second term C(H_(ref)S+N_(ref)) represents a model of the reference signal in the cepstral domain.

[0085] Turning now to FIG. 6, a noise adaptation system 60 capable of performing noise adaptation in a speech recognition system (not shown) is shown. Generally, noise adaptation system 60 uses a training speech signal 75 resulting from a speaker 62 in a recognition environment 64, and a target speech signal 79 (also referred to as an “input speech signal”) resulting from speaker 62 in a recognition environment 66. The training speech signal 75 is shown as having a convolutional noise component H_(ref) resulting from training channel 72, and an additive noise component N_(ref) as incorporated at summing module 74. Similarly, the target noise signal 79 has a convolutional noise component H_(tar) resulting from recognition channel 76 and an additive noise component N_(tar) as incorporated at summer 78.

[0086] The channels 72, 76 will typically incorporate various signal processing devices such as microphones, telephone lines, etc. The difficulty with noise adaptation arises when the recognition channel 76 has different characteristics from the training channel 72. In such cases, the target convolutional noise component H_(tar) will differ from the reference convolutional noise component H_(ref).

[0087] In one configuration of the present invention, a method is provided to jointly compensate for both additive and convolutional noises at each signal frame of an observed, or target, signal in the feature domain. A first-order expansion is used to approximate the non-linear compensation function:

Φ(C(H _(ref) ·S+N _(ref)), C(H _(tar) ·S+N _(tar)))  (8)

[0088] where C(·) is the cepstral operator, S represents a clean version of the target speech signal, H_(ref) is the channel frequency response for the training environment, H_(tar) is the channel frequency response of the test environment, N_(ref) is the additive noise for the training environment, and N_(tar) is the additive noise for the test environment. (The term “test environment,” as used herein, is used only by convention. The term “test environment” is also intended to encompass other recognition environments, for example, the environment illustrated by FIG. 1.)

[0089] The first order linear approximation of Φ is: $\begin{matrix} {{\begin{matrix} {{\hat{C}\left( {{H_{ref}S} + N_{ref}} \right)} = \left. {{C\left( {{H_{tar}S} + N_{tar}} \right)} + \quad \frac{\partial{C\left( {{H_{tar}S} + N} \right)}}{\partial N}} \middle| {}_{N = N_{tar}}\left( {N_{ref} - N_{tar}} \right) \right.} \\ \left. {+ \quad \frac{\partial{C\left( {{H\quad S} + N_{tar}} \right)}}{\partial H}} \middle| {}_{H = H_{tar}}{\left( {H_{ref} - H_{tar}} \right).} \right. \end{matrix}{{Let}:}}\quad} & (9) \\ {J_{N} = {\left. \frac{\partial{C\left( {{H_{tar} \cdot S} + N} \right)}}{\partial N} \right|_{N = N_{tar}} = {F^{\dagger}\frac{1}{{H_{tar} \cdot S} + N_{tar}}}}} & (10) \\ {{J_{H} = {\left. \frac{\partial{C\left( {{H \cdot S} + N_{tar}} \right)}}{\partial H} \right|_{N = N_{tar}} = {F^{\dagger}\frac{S}{{H_{tar} \cdot S} + N_{tar}}}}},} & (11) \end{matrix}$

[0090] where F^(†) is a decorrelating transform matrix such as a discrete cosine transform. (Matrix F^(†) may be complex, and another matrix F, also possibly complex, can readily be determined such that FF^(†)=I, the identity matrix. F^(†) is thus the inverse conjugate of matrix F.) Thus, one configuration of the present invention estimates both the additive noise bias ΔN=N_(ref)−N_(tar) and the channel bias ΔH=H_(ref)−H_(tar). Equation 10 allows J_(N) to be directly determined, in one configuration, from the noisy target speech signal H_(tar)·S+N_(tar) as $J_{N} = {F^{\dagger}{\frac{1}{{H_{tar} \cdot S} + N_{tar}}.}}$

[0091] In one configuration of a feature Jacobian adaptation module 100 of the present invention and referring to FIG. 7, a conventional estimate of additive noise bias ΔN=N_(ref)−N_(tar) is made during silence segments of the speech signal. This additive noise bias estimate is provided to an adaptive noise compensation module 102. To estimate the channel bias ΔH, a speech signal partially adapted to the test environment in additive noise is computed. For example, a first order approximation is determined by noise compensation module 102 using: $\begin{matrix} \begin{matrix} {{C\left( {{H_{tar} \cdot S} + N_{ref}} \right)} = \left. {{C\left( {{H_{tar} \cdot S} + N_{tar}} \right)} + \frac{\partial{C\left( {{H_{tar} \cdot S} + N} \right)}}{\partial N}} \middle| {}_{N = N_{tar}}\left( {N_{ref} - N_{tar}} \right) \right.} \\ {{= {{C\left( {{H_{tar} \cdot S} + N_{tar}} \right)} + {J_{N}\Delta \quad N}}},} \end{matrix} & (12) \end{matrix}$

[0092] where J_(N) is a noise compensation matrix that is readily determinable because it depends only on the observed signal (i.e., the target speech signal, see equation 10), and C(H_(tar)·S+N_(tar)) is the cepstrum of the observed signal.

[0093] Next, the convolutional noise bias ΔH=H_(ref)−H_(tar) is estimated by channel estimation block 104 using the “partially” adapted signal: $\begin{matrix} {{C\left( {{H_{tar} \cdot S} + N_{ref}} \right)} = \left. {{C\left( {{H_{ref} \cdot S} + N_{ref}} \right)} + \frac{\partial{C\left( {{H \cdot S} + N_{ref}} \right)}}{\partial H}} \middle| {}_{H = H_{ref}}\left( {\Delta \quad H} \right) \right.} & (13) \end{matrix}$

[0094] where C(H_(tar)·S+N_(ref)) is the “partially” adapted signal calculated in the previous step, and C(H_(ref)·S+N_(ref)) is the cepstral model corresponding to the observed signal in the spectral domain. However, the model for the currently observed signal frame is not available to estimation block 104 because it has not yet been determined. Therefore, estimation block 104 uses the assumption that the channel is stationary within two consecutive frames, i.e., ΔH is evaluated by channel estimation block 104 using the previous frame information. output by convolutional bias module 106.

[0095] More particularly, channel estimation module 104 uses C(H_(tar)·S+N_(ref)) output by adaptive noise compensation module 102 from the previous signal frame to estimate H_(ref)·S+N_(ref) using the most likely partial path, up to the previously decoded frame. Viterbi decoding or a hidden Markov model (HMM) are known in the art, and are used in one configuration to determine the most likely partial path or “partial traceback.” The spectral domain model is determined from the model in the ceptral domain utilizing an inverse cepstral operator C⁻¹(·), wherein C⁻¹(x)=exp(F⁻¹x), F^(†) is a matrix, Ft is a decorrelating transform and the inverse conjugate of F, and FF⁵⁵⁴=I, where I is an identity matrix. Let: $\begin{matrix} {J_{P} = {\left. \frac{\partial{C\left( {{H \cdot S} + N_{ref}} \right)}}{\partial H} \right|_{H = H_{ref}} = {F^{\dagger}\frac{S}{{H_{ref} \cdot S} + N_{ref}}}}} & (14) \end{matrix}$

[0096] then, in one configuration, ΔH is estimated using matrix inverse J⁻¹ ₁:

ΔH=J ⁻¹ _(p) [C(H _(ref) ·S+N _(ref))−C(H _(tar) ·S+N _(ref))]  (15)

[0097] Joint noise and channel estimation module 106 uses the linear approximation of ψ given by equation (9) to compensate the observed signal for both additive and convolutional noises. The values ΔH produced by channel estimation module 104, the estimate of ΔN=N_(ref)−N_(tar) produced during silence segments of the speech signal, and the input value C(H_(tar)·S+N_(tar)) are used to produce the estimate Ĉ(H_(ref)S+N_(ref)).

[0098] Because the adaptation is performed each frame, configurations of the present invention are more robust against nonstationary noise and channels, when there is a “fine” estimate of additive noise. In addition, although modified at a higher rate, fewer parameters are modified, and only signal features are modified rather than all model features. Therefore, configurations of the present invention use less memory (e.g., random access memory or RAM), which is advantageous for small embedded systems. Moreover, because the model features are not modified, adapted model features need not be stored in memory.

[0099] In one configuration of the present invention and referring to FIG. 8, a reference model is compensated for convolutional noise in the cepstral domain (as part of joint compensation) utilizing feature Jacobian adaptation module 100. Convolutional module 82 provides an estimation of the convolutional bias and adapts the reference model with this estimation. The result is a convolutionally adapted model 96. Convolutionally adapted model 96 is then operated upon by additive noise module 80 to fully compensate reference model 70 for both additive and convolutional noise. Specifically, one configuration of convolutional noise module 82 includes a convolutional bias module 84 for estimating convolutional bias between a reference model 70 and a target speech signal 79. An adaptation matrix module 86 generates a channel adaptation matrix 88 based on a training speech signal. Channel adaptation matrix 88 is essentially a modified noise adaptation matrix 1−J_(c). Matrix J_(c) can be either a standard Jacobian matrix or an α-Jacobian matrix. Convolutional bias module 84 transforms the estimated convolutional bias with channel adaptation matrix 88. The convolutional noise module 82 further includes a summation module 90 coupled to convolutional bias module 84 for adding the transformed convolutional bias to reference model 70 in the cepstral domain. Target speech signal 79 is jointly compensated in the feature domain for channel and additive noise by feature Jacobian adaptation module 100 after conversion to the cepstral domain by cepstral analysis module 108 to produce compensated signal 97.

[0100] An adaptation matrix module 86 generates a channel adaptation matrix 88 based on the training speech signal. The channel adaptation matrix 88 is essentially a modified noise adaptation matrix 1−J_(c). It is important to note that J_(c) can either be a standard Jacobian matrix or an α-Jacobian matrix as described above. The convolutional bias module 84 transforms the estimated convolutional bias with the channel adaptation matrix 88. The convolutional noise module 82 further includes a summation module 90 coupled to the convolutional bias module 84 for adding the transformed convolutional bias to the reference model 70 in the cepstral domain.

[0101] Computation of the Convolutional Bias

[0102] In order to estimate the convolutional bias, let us assume that the Gaussian alignment between the reference models and the signal is known. We describe two possible approaches to compute the convolutional bias, based on this assumption:

[0103] I. First Approach

[0104] If we assume that H_(tar)S

N_(tar), then it is possible to average the segments of the signal corresponding to speech units, in order to obtain: ${\hat{C}\left( S_{tar} \right)} = {{\frac{1}{T}{\sum\limits_{t = 1}^{T}\left( {C\left( {H_{tar} \cdot S} \right)} \right)}} = {{C\left( H_{tar} \right)} + {\frac{1}{T}{\sum\limits_{i = 1}^{T}{{C\left( S_{t} \right)}.}}}}}$

[0105] Similarly, it should be possible to compute the term Ĉ(S_(ref)) by averaging the same reference, i.e., clean, signal. However, this signal is generally not available, as only the noisy (target) signal is known. We then have to estimate this reference signal. Such an estimate may be obtained with the use of a Gaussian alignment between the models and the signal. Therefore, for each frame, the Gaussian density aligned with the target frame C(H_(tar)S_(t)) represents the corresponding reference frame C(H_(ref)S_(t)). It is then possible to compute: ${\hat{C}\left( S_{ref} \right)} = {{\frac{1}{T}{\sum\limits_{t = 1}^{T}\left( {C\left( {H_{ref} \cdot S} \right)} \right)}} = {{C\left( H_{ref} \right)} + {\frac{1}{T}{\sum\limits_{i = 1}^{T}{{C\left( S_{t} \right)}.}}}}}$

[0106] By subtracting the two previous equations, we obtain:

C(H _(tar))−C(H _(ref))=Ĉ(S _(tar))−Ĉ(S _(ref)).  (16)

[0107] In practice, to compute the channel bias as indicated by the above equation, we need the Gaussian alignment of the current sentence, as given by the recognizer. In order to avoid using a two-pass recognition system, we have decided to adapt the current sentence with the adaptive bias computed on the previous one. This makes the system more sensitive to a change of the environment, as for example when a different speaker pronounces the previous and the current sentence. However, the advantage of this approximation is that the adaptation is still very fast and only requires a single recognition pass.

[0108] Convolutional noise module 82 can further include a Gaussian alignment module 92, between feature Jacobian adaptation module 100 and convolutional bias module 84, for segmenting the target speech signal into target speech segments and target silence segments. Gaussian alignment module 92 operates on compensated signal 97 and produces output 99, which is fed to convolutional bias module 84. (When Gaussian alignment module 92 is not present, compensated signal 97 is fed to convolutional bias module 84 instead of output 99.) While the segmentation function is typically included within the speech recognizer, it is described here as part of the convolutional noise module 82 for purposes of discussion. In fact, the particular location of many of the components described herein may vary without parting from the nature and scope of the invention. The convolutional bias module 84 therefore averages the target speech signals and Gaussian data corresponding to the reference model 70. The convolutional bias module 84 further calculates a difference between the average for the Gaussian data and the average for the target speech segments. The result is a convolutional bias C(H_(tar))−C(H_(ref)) than can be added to the reference model 70 in the cepstral domain after transformation by the channel adaptation matrix.

[0109] II. Second Approach

[0110] A preferred incremental solution to estimating the convolutional bias allows us to take into account the target noise N_(tar). This method makes use of a previous estimate of the convolutional bias (computed, for example, on the previous sentence), and improves this estimate by using the signal of the current sentence. The convolutional bias is therefore estimated incrementally, from one sentence to the next one, and is likely to improve so long as the speaker or the environment does not change.

[0111] Averaging the signal of the speech segments of the current sentence leads us to: $\begin{matrix} {{\hat{C}\left( S_{tar} \right)} = {\frac{1}{T}{\sum\limits_{t = 1}^{T}\left( {C\left( {{H_{tar} \cdot S_{t}} + N_{tar}} \right)} \right)}}} \\ {= {\frac{1}{T}{\sum\limits_{t = 1}^{T}\left( {{C\left( H_{tar} \right)} + {C\left( {S_{t} + \frac{N_{tar}}{H_{tar}}} \right)}} \right)}}} \\ {= {{C\left( H_{tar} \right)} + {\frac{1}{T}{\sum\limits_{t = 1}^{T}{C\left( {S_{t} + \frac{N_{tar}}{H_{tar}}} \right)}}}}} \end{matrix}\quad$

[0112] On the previous sentence, the adapted models $C\left( {{H_{ref}S} + {\frac{H_{ref}}{H_{tar}}N_{tar}}} \right)$

[0113] have already been estimated. It is then possible to compute the average of the reference frames using this set of models: $\begin{matrix} {{\hat{C}\left( S_{ref} \right)} = {\frac{1}{T}{\sum\limits_{t = 1}^{T}\quad \left( {C\left( {{H_{ref} \cdot S_{t}} + {\frac{H_{ref}}{H_{tar}}N_{tar}}} \right)} \right)}}} \\ {= {\frac{1}{T}{\sum\limits_{t = 1}^{T}\quad \left( {{C\left( H_{ref} \right)} + {C\left( {S_{t} + \frac{N_{tar}}{H_{tar}}} \right)}} \right)}}} \\ {= {{C\left( H_{ref} \right)} + {\frac{1}{T}{\sum\limits_{t = 1}^{T}\quad {C\left( {S_{t} + \frac{N_{tar}}{H_{tar}}} \right)}}}}} \end{matrix}$

[0114] Subtracting the two previous equations gives us the channel bias represented by equation (16). With this method, we have to assume that the target and reference channels of the first sentence are identical.

[0115] It is important to note that the above joint compensation approach enjoys many of the benefits associated with α-Jacobian Adaptation described for additive noise compensation alone. As already discussed, α-Jacobian Adaptation finds its roots in the Jacobian Adaptation algorithm. α-Jacobian Adaptation differs from Jacobian Adaptation in the way the approximation is realized: the latter makes use of the linear function that best approximates PMC in the training conditions, whereas the former experimentally computes a linear function that better approximates PMC for a selected set of possible testing conditions. As a result, α-Jacobian Adaptation performs better than classical Jacobian Adaptation for real testing conditions.

[0116] We have then decreased by more than a half the time and memory complexity of this algorithm by reducing, with the use of Principal Component Analysis, the number of required transformation matrices, without degrading the recognition results.

[0117] Because the transformation performed on the observed signal in the cepstral domain is mathematically equivalent to a linear filtering in the time domain, the first impression of one of ordinary skill in the art might be that configurations of the present invention such as those illustrated in FIGS. 7 and 8 are sub-optimal in terms of minimizing mean square error. However, this has not been found to be the case in practice in configurations of the present invention.

[0118] The description of the invention is merely exemplary in nature and, thus, variations that do not depart from the gist of the invention are intended to be within the scope of the invention. Such variations are not to be regarded as a departure from the spirit and scope of the invention. 

What is claimed is:
 1. A method for performing noise adaptation of a target speech signal input to a speech recognition system, said target speech signal containing both additive and convolutional noises, said method comprising: estimating an additive noise bias and a convolutional noise bias; in said target speech signal; and jointly compensating the target speech signal for the additive and convolutional noise biases in a feature domain.
 2. A method in accordance with claim 1 wherein said target speech signal comprises a plurality of frames, and further wherein said estimating a convolutional noise bias comprises determining a speech signal partially adapted to the test environment in additive noise; and utilizing the partially adapted speech signal to estimate the convolutional noise bias.
 3. A method in accordance with claim 2, wherein said determining a speech signal partially adapted to the test environment in additive noise comprises determining a first order approximation as: $\begin{matrix} {{{{{C\left( {{H_{tar} \cdot S} + N_{ref}} \right)} = {{C\left( {{H_{tar} \cdot S} + N_{tar}} \right)} + \frac{\partial{C\left( {{H_{tar} \cdot S} + N} \right)}}{\partial N}}}}_{N = N_{tar}}\left( {N_{ref} - N_{tar}} \right)},} \\ {{= {{C\left( {{H_{tar} \cdot S} + N_{tar}} \right)} + {J_{N}\Delta \quad N}}},} \end{matrix}$

wherein: C(·) is the cepstral operator; H_(tar) is a channel frequency response for a test environment; N_(ref) is an additive noise for a training environment; N_(tar) is an additive noise for the test environment; S represents a clean version of the target speech signal; ${{J_{N}\quad {is}\quad \frac{\partial{C\left( {{H_{tar} \cdot S} + N} \right)}}{\partial N}}}_{N = N_{tar}},{{a\quad {noise}\quad {compensation}\quad {matrix}};}$

ΔN is (N_(ref)−N_(tar)); and C(H_(tar)·S+N_(ref)) is said partially adapted speech signal.
 4. A method in accordance with claim 3 further comprising determining noise compensation matrix J_(N) as: ${J_{N} = {F^{\dagger}\frac{1}{{H_{tar} \cdot S} + N_{tar}}}},$

where F^(†) is a decorrelating transform and H_(tar)·S+N_(tar) is the noisy target speech signal.
 5. A method in accordance with claim 3 wherein said partially adapted speech signal utilized to estimate the convolutional noise bias of one of said frames of said target speech signal is a partially adapted speech signal determined from a previous said signal frame.
 6. A method in accordance with claim 5 wherein said estimating a convolutional noise bias further comprises determining a model H_(ref)·S+N_(ref) corresponding to said target speech signal in the spectral domain, wherein H_(ref) is a channel frequency response for a training environment.
 7. A method in accordance with claim 6 wherein said determining a model corresponding to said target speech signal in the spectral domain comprises utilizing Viterbi decoding to evaluate a most likely partial path.
 8. A method in accordance with claim 7 wherein said convolutional noise bias ΔH=H_(ref)−H_(tar) is determined as: ΔH=J ⁻¹ _(p) [C(H _(ref) ·S+N _(ref))−C(H _(tar) ·S+N _(ref))], wherein: J⁻¹ _(p) is a matrix inverse, in which ${{{J_{P} = \frac{\partial{C\left( {{H \cdot S} + N_{ref}} \right)}}{\partial H}}}_{H = H_{ref}} = {F^{\dagger}\frac{S}{{H_{ref} \cdot S} + N_{ref}}}};$

and F^(†) is a decorrelating transform.
 9. A method in accordance with claim 8 wherein F^(†) is a discrete cosine transform.
 10. A method in accordance with claim 2 wherein said partially adapted speech signal utilized to estimate the convolutional noise bias of one of said frames of said target speech signal is a partially adapted speech signal determined from a previous said signal frame.
 11. A method in accordance with claim 10 wherein said estimating a convolutional noise bias further comprises determining a model corresponding to said target speech signal in the spectral domain.
 12. A method in accordance with claim 11 wherein said determining a model corresponding to said target speech signal in the spectral domain comprises utilizing Viterbi decoding to evaluate a most likely partial path.
 13. A method in accordance with claim 12 further comprising determining said model in the spectral domain from a model in the cepstral domain utilizing an inverse cepstral operator C⁻¹(·), wherein C⁻¹(x)=exp(F⁻¹x), F is a matrix, F^(†) is a decorrelating transform and the inverse conjugate of F, and FF^(†)=I, where I is an identity matrix.
 14. A speech recognition apparatus including noise adaptation of a target speech signal input to said apparatus, said target speech signal containing both additive and convolutional noises, said apparatus configured to: estimate an additive noise bias and a convolutional noise bias in said target speech signal; and jointly compensate the target speech signal for the additive and convolutional noise biases in a feature domain.
 15. An apparatus in accordance with claim 14 wherein said target speech signal comprises a plurality of frames, and further wherein to estimate a convolutional noise bias, said apparatus is configured to: determine a speech signal partially adapted to the test environment in additive noise; and utilize the partially adapted speech signal to estimate the convolutional noise bias.
 16. An apparatus in accordance with claim 15, wherein to determine a speech signal partially adapted to the test environment in additive noise said apparatus is configured to determine a first order approximation as: $\begin{matrix} {{{{{C\left( {{H_{tar} \cdot S} + N_{ref}} \right)} = {{C\left( {{H_{tar} \cdot S} + N_{tar}} \right)} + \frac{\partial{C\left( {{H_{tar} \cdot S} + N} \right)}}{\partial N}}}}_{N = N_{tar}}\left( {N_{ref} - N_{tar}} \right)},} \\ {{= {{C\left( {{H_{tar} \cdot S} + N_{tar}} \right)} + {J_{N}\Delta \quad N}}},} \end{matrix}$

wherein: C(·) is the cepstral operator; H_(tar) is a channel frequency response for a test environment; N_(ref) is an additive noise for a training environment; N_(tar) is an additive noise for the test environment; S represents a clean version of the target speech signal; ${{J_{N}\quad {is}\quad \frac{\partial{C\left( {{H_{tar} \cdot S} + N} \right)}}{\partial N}}}_{N = N_{tar}},{{a\quad {noise}\quad {compensation}\quad {matrix}};}$

ΔN is (N_(ref)−N_(tar)); and C(H_(tar)·S+N_(ref)) is said partially adapted speech signal. 17 An apparatus in accordance with claim 16 further configured to determine noise compensation matrix J_(N) as: ${J_{N} = {F^{\dagger}\frac{1}{{H_{tar} \cdot S} + N_{tar}}}},$

where F^(†) is a decorrelating transform and H_(tar)·S+N_(tar) is the noisy target speech signal.
 18. An apparatus in accordance with claim 16 wherein said partially adapted speech signal utilized to estimate the convolutional noise bias of one of said frames of said target speech signal is a partially adapted speech signal determined from a previous said signal frame.
 19. An apparatus in accordance with claim 18 wherein to estimate a convolutional noise bias, said apparatus is further configured to determine a model H_(ref)·S+N_(ref) corresponding to said target speech signal in the spectral domain, wherein H_(ref) is a channel frequency response for a training environment.
 20. An apparatus in accordance with claim 19 wherein to determine a model corresponding to said target speech signal in the spectral domain, said apparatus is configured to utilize Viterbi decoding to evaluate a most likely partial path.
 21. An apparatus in accordance with claim 20 configured to determine said convolutional noise bias ΔH=H_(ref)−H_(tar) as: ΔH=J ⁻¹ _(p[C)(H _(ref) ·S+N _(ref))−C(H _(tar) ·S+N _(ref))], wherein: J⁻¹ _(p) is a matrix inverse, in which ${{{J_{P} = \frac{\partial{C\left( {{H \cdot S} + N_{ref}} \right)}}{\partial H}}}_{H = H_{ref}} = {F^{\dagger}\frac{S}{{H_{ref} \cdot S} + N_{ref}}}};$

and F^(†) is a decorrelating transform.
 22. An apparatus in accordance with claim 21 wherein F^(†) is a discrete cosine transform.
 23. An apparatus in accordance with claim 22 wherein said partially adapted speech signal utilized to estimate the convolutional noise bias of one of said frames of said target speech signal is a partially adapted speech signal determined from a previous said signal frame.
 24. An apparatus in accordance with claim 23 wherein to estimate a convolutional noise bias, said apparatus is further configured to determine a model corresponding to said target speech signal in the spectral domain.
 25. An apparatus in accordance with claim 24 wherein to determine a model corresponding to said target speech signal in the spectral domain, said apparatus is configured to utilize Viterbi decoding to evaluate a most likely partial path. 26 An apparatus in accordance with claim 25 further configured to said model in the spectral domain from a model in the cepstral domain inverse cepstral operator C⁻¹(·), wherein C⁻¹(x)=exp(F⁻¹x), F is a matrix, F^(†) is a decorrelating transform and the inverse conjugate of F, and FF^(†)=I, where I is an identity matrix. 